Stability and instability of fluid models for reentrant lines
Mathematics of Operations Research
Polling Systems in Heavy Traffic: a Bessel Process Limit
Mathematics of Operations Research
Stability of two families of queueing networks and a discussion of fluid limits
Queueing Systems: Theory and Applications
An introduction to large deviations for communication networks
IEEE Journal on Selected Areas in Communications
Critical Thresholds for Dynamic Routing in Queueing Networks
Queueing Systems: Theory and Applications
Continuous-Review Tracking Policies for Dynamic Control of Stochastic Networks
Queueing Systems: Theory and Applications
Performance Evaluation and Policy Selection in Multiclass Networks
Discrete Event Dynamic Systems
Queueing Dynamics and Maximal Throughput Scheduling in Switched Processing Systems
Queueing Systems: Theory and Applications
In Search of Sensitivity in Network Optimization
Queueing Systems: Theory and Applications
Stochastic Networks: Admission and Routing Using Penalty Functions
Queueing Systems: Theory and Applications
Queueing Systems: Theory and Applications
Optimal Control of a High-Volume Assemble-to-Order System
Mathematics of Operations Research
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This paper describes a family of discrete-review policies for scheduling open multiclass queueing networks. Each of the policies in the family is derived from what we call a dynamic reward function: such a function associates with each queue length vector q and each job class k a positive value r_k(q), which is treated as a reward rate for time devoted to processing class k jobs. Assuming that each station has a traffic intensity parameter less than one, all policies in the family considered are shown to be stable. In such a policy, system status is reviewed at discrete points in time, and at each such point the controller formulates a processing plan for the next review period, based on the queue length vector observed. Stability is proved by combining elementary large deviations theory with an analysis of an associated fluid control problem. These results are extended to systems with class dependent setup times as well as systems with alternate routing and admission control capabilities.